Cooperative multiscale aging in a ferromagnet/antiferromagnet bilayer

Anisotropic magnetoresistance measurements show that the magnetization state in epitaxial ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}/{\mathrm{Fe}}_{50}{\mathrm{Mn}}_{50}$ bilayers exhibits aging over a wide range of temperatures and magnetic fields. The observed power-law time dependence indicates that aging is characterized by a wide range of activation time scales. Aging characteristics are also inconsistent with a superposition of independent activation barriers expected for Arrhenius-type relaxation. The observed effects indicate a fundamental connection with the critical phenomena in complex condensed matter systems.

Figure 1

(a) Dependence of resistance on the in-plane orientation of $H$, at $T=295$ K, $H=100$ Oe (solid symbols), and 5 K, $H=2$ kOe (open symbols). $\theta =0$ is perpendicular to current. (b) Temperature dependence of magnetoresistance, determined from $R\left(\theta \right)$ obtained at $H=2$ kOe, after initial field cooling at $H=500$ Oe, $\theta =0$. (c) Magnetoelectronic hysteresis loop obtained at 5 K, after four similar prior loops. Curves: fits based on the exchange field model described in the text. Coercive fields $H_{-}$ and $H_{+}$ are labeled. (d) Coercivity $H_C$ and exchange bias field $H_E$ vs $T$.

Figure 2

Aging at $T=5$ K. (a) Symbols: time evolution of resistance $R$ at $H_f=-300$ Oe, after prior aging at $H_i=350$ Oe for 1000 s. Curve: fitting with the power-law dependence $R\left(t\right)=R_0+A{t}^{-c}, R_0=3.496 \mathrm{\Omega }, A=0.011$, and $c=0.081$. Inset: $R-R_0$ vs $t$ plotted on the log-log scale. (b) Seven sequential aging cycles at $H_f=-500$ Oe, as labeled, each preceded by aging at $H_i=350$ Oe for 1000 s. (c), (d) $c$ (c) and $R_0$ (d) vs aging cycle, immediately after cooling from RT. Error bars show the fitting uncertainty.

Figure 3

(a) $R$ vs $t$ at $T=5$ K, $H_f=150$ Oe, after prior aging at $H_i=-300$ Oe over the time intervals $\mathrm{\Delta }{t}_i=500$ s (bottom curve), 200 s, 100 s, 51 s, 21 s, 11 s, 6 s, and 3 s (top curve). (b) $c$ vs $\mathrm{\Delta }{t}_i$. (c) Symbols: $A$ vs $\mathrm{\Delta }{t}_i$; line: logarithmic fit to the data.

Figure 4

Dependence on $H$ at $T=5$ K. The duration of aging for both field directions was 1000 s, with $H_i=350$ Oe ($-500$ Oe) for $H_f>0$ ($<0$). (a) $c$ vs $H$. Error bars show the fitting uncertainty. (b) Symbols: $R(t=1s)-R_0$ vs $H$. Curves: fitting of the $\left|H\right|>200$ Oe data, based on the effective exchange field model described in the text.

Figure 5

(a) Symbols: $R$ vs $t$ at $T=210$ K, $H_f=-65$ Oe, and $H_f=55$ Oe, as labeled. Curves: fittings using the power-law dependence with $c=0.126$ and $0.246$, respectively. (b) $H_f$ vs $T$ used in the aging measurements. (c), (d) $c$ (c) and $A$ (d) vs $T$. Filled (open) symbols are for $H_f>0 [H_f<0]$.